Problem: A group of adults and kids went to see a movie. Tickets cost $$7.50$ each for adults and $$2.00$ each for kids, and the group paid $$42.00$ in total. There were $2$ fewer adults than kids in the group. Find the number of adults and kids in the group.
Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${7.5x+2y = 42}$ ${x = y-2}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-2}$ for $x$ in the first equation. ${7.5}{(y-2)}{+ 2y = 42}$ Simplify and solve for $y$ $ 7.5y-15 + 2y = 42 $ $ 9.5y-15 = 42 $ $ 9.5y = 57 $ $ y = \dfrac{57}{9.5} $ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into ${x = y-2}$ to find $x$ ${x = }{(6)}{ - 2}$ ${x = 4}$ You can also plug ${y = 6}$ into ${7.5x+2y = 42}$ and get the same answer for $x$ ${7.5x + 2}{(6)}{= 42}$ ${x = 4}$ There were $4$ adults and $6$ kids.